Probabilistic Physics-Guided Machine Learning With Missing Data: Applications in Additive Manufacturing

Abstract Machine learning (ML) is increasingly utilized in materials and structural analysis. However, for an ML model to perform effectively, it requires a large amount of high-quality data for training. When experimental or simulation data are insufficient, training data can be sourced from literature. However, literature data often come from diverse sources (e.g., different testing equipment and materials) and lack standardization, leading to significant data variability and missing information. This work aims to develop a physics-guided machine learning model that accounts for these data variations and missing data. We focus on the probabilistic fatigue life prediction of additively manufactured (AM) Ti-6Al-4V, considering the influence of process parameters. Fatigue data for AM Ti-6Al-4V, both in as-built and annealed conditions, were collected from extensive literature, capturing various process parameters (e.g., scanning speed, laser power, hatch space, layer thickness, heat temperature, and heat time). A Probabilistic Physics-Guided Neural Network (PPgNN) is proposed to model these data, with the following novelties: (1) Handling Data Variability: Given the wide range of data sources, there are significant variations for the same variables. The PPgNN can be trained on noisy literature data and predict both the mean and variance of fatigue life. (2) Addressing Missing Data: Due to inconsistencies in how data are reported, some process parameters are available in some literature but missing in others. The model can be trained with incomplete datasets and adapt when additional information becomes available. (3) Incorporating Domain Knowledge: Existing fatigue analysis knowledge is integrated into the ML model to guide learning and prediction. The PPgNN includes constraints on model parameters to ensure the generated probabilistic stress-life (P-S-N) curves have physics-consistent curvature and non-constant variance. The results demonstrate that PPgNN effectively manages uncertainties arising from data variations and missing information, producing physics-consistent probabilistic predictions. A global sensitivity analysis using the Sobol sensitivity was also performed to assess the importance of the process parameters.